Machin-like formulae
M000000566
$$\pi=8\arctan\left(\frac{1}{2}\right)-4\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{31}\right)+4\arctan\left(\frac{1}{43}\right)$$
Compact formula
8[2] - 4[5] + 4[31] + 4[43]
Lehmer's measure
6.03532